arXiv subjects

David F. Chernoff

Publications and source records attributed to David F. Chernoff.

At least 19 recordsLinked to original sources

arXiv2024

Modeling the Beam of Gravitational Radiation from a Cosmic String Loop

We investigate exact and approximate techniques to calculate the emission of gravitational radiation from cosmic string loops in order to generate beam models covering the entire celestial sphere for a wide range of modes $m$. One approach entails summing over contributions of stationary and nearly-stationary points of individual, factorized, left- and right-moving modes. This "multipoint method" generalizes traditional methods that rely on expansions around exact stationary points of mode products. A second complementary approach extends the method of steepest descent to generate an asymptotic description of the beam as $m \to \infty$. We present example calculations of the emission of power from cusp-containing loops and compare the results with those obtained by numerically exact techniques as well as by previous approaches. The multipoint method achieves its best results at an intermediate range of modes, improving over previous methods in terms of accuracy. It handles the emission from all regions of the loop not just those near cusps. We demonstrate this capability by making a detailed study of the "pseudocusp" phenomenon.

astro-ph.CO↗

arXiv2023

Waveform Modelling for the Laser Interferometer Space Antenna

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome.

gr-qc↗

arXiv2020

Periodic Fast Radio Bursts from Axion Emission by Cosmic Superstrings

We propose that the periodic fast radio bursts of FRB 180916.J0158+65 are sourced by axion emission (mass $m_{a} \sim 10^{-14}$ eV) from cosmic superstrings. Some of the emitted axions are converted to photons by magnetic fields as they travel along the line of sight to Earth. An impulsive burst of axion emission generates a photon signal typically lasting for milliseconds and varying with frequency in the observed manner. We find a range of parameters in our cosmic string network model consistent with the properties of FRB 180916.J0158+65. We suggest followup gravitational wave observations to test our model.

astro-ph.CO↗

arXiv2019

Prospects of Cosmic Superstring Detection through Microlensing of Extragalactic Point-Like Sources

The existence of cosmic superstrings may be probed by astronomical time domain surveys. When crossing the line of sight to point-like sources, strings produce a distinctive microlensing signature. We consider two avenues to hunt for a relic population of superstring loops: frequent monitoring of (1) stars in Andromeda, lensed by loops in the haloes of the Milky-Way and Andromeda and (2) supernovae at cosmological distances, lensed by loops in the intergalactic medium. We assess the potential of such experiments to detect and/or constrain strings with a range of tensions, $10^{-15} \lesssim G μ/c^2 \lesssim 10^{-6}$. The practical sensitivity is tied to cadence of observations which we explore in detail. We forecast that high-cadence monitoring of $\sim 10^5$ stars on the far side of Andromeda over a year-long period will detect microlensing events if $Gμ/c^2 \sim 10^{-13}$, while $\sim 10^6$ stars will detect events if $10^{-13.5} <Gμ/c^2 < 10^{-11.5}$; the upper and lower bounds of the accessible tension range continue to expand as the number of stars rises. We also analyse the ability to reject models in the absence of fluctuations. While challenging, these studies are within reach of forthcoming time-domain surveys. Supernova observations can hypothetically constrain models with $10^{-12} < Gμ/c^2 < 10^{-6}$ without any optimisation of the survey cadence. However, the event rate forecast suggests it will be difficult to reject models of interest. As a demonstration, we use observations from the Pantheon Type Ia supernova cosmology data-set to place modest constraints on the number density of cosmic superstrings in a poorly tested region of the parameter space.

astro-ph.CO↗

arXiv2018

Gravitational backreaction on a cosmic string: Formalism

We develop a method for computing the linearized gravitational backreaction for Nambu-Goto strings using a fully covariant formalism. We work with equations of motion expressed in terms of a higher dimensional analog of the geodesic equation subject to self-generated forcing terms. The approach allows arbitrary spacetime and worldsheet gauge choices for the background and perturbation. The perturbed spacetime metric may be expressed as an integral over a distributional stress-energy tensor supported on the string worldsheet. By formally integrating out the distribution, this quantity may be re-expressed in terms of an integral over the retarded image of the string. In doing so, one must pay particular attention to contributions that arise from the field point and from non-smooth regions of the string. Then, the gradient of the perturbed metric decomposes into a sum of boundary and bulk terms. The decomposition depends upon the worldsheet coordinates used to describe the string, but the total is independent of those considerations. We illustrate the method with numerical calculations of the self-force at every point on the worldsheet for loops with kinks, cusps and self-intersections using a variety of different coordinate choices. For field points on smooth parts of the worldsheet the self-force is finite. As the field point approaches a kink or cusp the self-force diverges, but is integrable in the sense that the displacement of the worldsheet remains finite. As a consistency check, we verify that the period-averaged flux of energy-momentum at infinity matches the direct work the self-force performs on the string. The methodology can be applied to address many fundamental questions for string loop evolution.

gr-qc↗

arXiv2018

Bayesian Methods for Analysis and Adaptive Scheduling of Exoplanet Observations

We describe work in progress by a collaboration of astronomers and statisticians developing a suite of Bayesian data analysis tools for extrasolar planet (exoplanet) detection, planetary orbit estimation, and adaptive scheduling of observations. Our work addresses analysis of stellar reflex motion data, where a planet is detected by observing the "wobble" of its host star as it responds to the gravitational tug of the orbiting planet. Newtonian mechanics specifies an analytical model for the resulting time series, but it is strongly nonlinear, yielding complex, multimodal likelihood functions; it is even more complex when multiple planets are present. The parameter spaces range in size from few-dimensional to dozens of dimensions, depending on the number of planets in the system, and the type of motion measured (line-of-sight velocity, or position on the sky). Since orbits are periodic, Bayesian generalizations of periodogram methods facilitate the analysis. This relies on the model being linearly separable, enabling partial analytical marginalization, reducing the dimension of the parameter space. Subsequent analysis uses adaptive Markov chain Monte Carlo methods and adaptive importance sampling to perform the integrals required for both inference (planet detection and orbit measurement), and information-maximizing sequential design (for adaptive scheduling of observations). We present an overview of our current techniques and highlight directions being explored by ongoing research.

astro-ph.IM↗

arXiv2018

Detection of Low Tension Cosmic Superstrings

Cosmic superstrings of string theory differ from conventional cosmic strings of field theory. We review how the physical and cosmological properties of the macroscopic string loops influence experimental searches for these relics from the epoch of inflation. The universe's average density of cosmic superstrings can easily exceed that of conventional cosmic strings having the same tension by two or more orders of magnitude. The cosmological behavior of the remnant superstring loops is qualitatively distinct because the string tension is exponentially smaller than the string scale in flux compactifications in string theory. Low tension superstring loops live longer, experience less recoil (rocket effect from the emission of gravitational radiation) and tend to cluster like dark matter in galaxies. Clustering enhances the string loop density with respect to the cosmological average in collapsed structures in the universe. The enhancement at the Sun's position is $\sim 10^5$. We develop a model encapsulating the leading order string theory effects, the current understanding of the string network loop production and the influence of cosmological structure formation suitable for forecasting the detection of superstring loops via optical microlensing, gravitational wave bursts and fast radio bursts. We evaluate the detection rate of bursts from cusps and kinks by LIGO- and LISA-like experiments. Clustering dominates rates for $G μ< 10^{-11.9}$ (LIGO cusp), $G μ<10^{-11.2}$ (LISA cusp), $G μ< 10^{-10.6}$ (LISA kink); we forecast experimentally accessible gravitational wave bursts for $G μ>10^{-14.2}$ (LIGO cusp), $G μ>10^{-15}$ (LISA cusp) and $G μ>10^{- 14.1}$ (LISA kink).

astro-ph.CO↗

arXiv2017

Pulsar Timing Perturbations from Galactic Gravitational Wave Bursts with Memory

Pulsar timing arrays (PTAs) are used to search for long-wavelength gravitational waves (GWs) by monitoring a set of spin-stable millisecond pulsars. Most theoretical analyses assume that the relevant GW sources are much more distant from Earth than the pulsars comprising the array. Unlike ground- or solar system-based GW detectors, PTAs might well contain embedded GW sources. We derive the PTA response from sources at any distance, with a specific focus on GW bursts with memory (BWMs). We consider supernovae and compact binary mergers as potential Galactic BWM sources and evaluate the signature for an array with pulsars in globular clusters or in the Galactic center. Understanding the response of PTAs to nearby sources of BWM is a step towards investigating other more complex Galactic sources.

astro-ph.GA↗

arXiv2014

Inflation, String Theory and Cosmology

At its very beginning, the universe is believed to have grown exponentially in size via the mechanism of inflation. The almost scale-invariant density perturbation spectrum predicted by inflation is strongly supported by cosmological observations, in particular the cosmic microwave background radiation. However, the universe's precise inflationary scenario remains a profound problem for cosmology and for fundamental physics. String theory, the most-studied theory as the final physical theory of nature, should provide an answer to this question. Some of the proposals on how inflation is realized in string theory are reviewed. Since everything is made of strings, some string loops of cosmological sizes are likely to survive in the hot big bang that followed inflation. They appear as cosmic strings, which can have intricate properties. Because of the warped geometry in flux compactification of the extra spatial dimensions in string theory, some of the cosmic strings may have tensions substantially below the Planck or string scale. Such strings cluster in a manner similar to dark matter leading to hugely enhanced densities. As a result, numerous fossil remnants of the low tension cosmic strings may exist within the galaxy. They can be revealed through the optical lensing of background stars in the near future and studied in detail through gravitational wave emission. We anticipate that these cosmic strings will permit us to address central questions about the properties of string theory as well as the birth of our universe.

astro-ph.CO↗

arXiv2014

Dynamically formed black hole+millisecond pulsar binaries in globular clusters

The discovery of a binary comprising a black hole (BH) and a millisecond pulsar (MSP) would yield insights into stellar evolution and facilitate exquisitely sensitive tests of general relativity. Globular clusters (GCs) are known to harbor large MSP populations and recent studies suggest that GCs may also retain a substantial population of stellar mass BHs. We modeled the formation of BH+MSP binaries in GCs through exchange interactions between binary and single stars. We found that in dense, massive clusters most of the dynamically formed BH+MSP binaries will have orbital periods of 2 to 10 days, regardless of the mass of the BH, the number of BHs retained by the cluster, and the nature of the GC's binary population. The size of the BH+MSP population is sensitive to several uncertain parameters, including the BH mass function, the BH retention fraction, and the binary fraction in GCs. Based on our models, we estimate that there are $0.6\pm0.2$ dynamically formed BH+MSP binaries in the Milky Way GC system, and place an upper limit on the size of this population of $\sim 10$. Interestingly, we find that BH+MSP binaries will be rare even if GCs retain large BH populations.

astro-ph.HE↗

arXiv2013

Cosmic String Loop Microlensing

Cosmic superstring loops within the galaxy microlens background point sources lying close to the observer-string line of sight. For suitable alignments, multiple paths coexist and the (achromatic) flux enhancement is a factor of two. We explore this unique type of lensing by numerically solving for geodesics that extend from source to observer as they pass near an oscillating string. We characterize the duration of the flux doubling and the scale of the image splitting. We probe and confirm the existence of a variety of fundamental effects predicted from previous analyses of the static infinite straight string: the deficit angle, the Kaiser-Stebbins effect, and the scale of the impact parameter required to produce microlensing. Our quantitative results for dynamical loops vary by O(1) factors with respect to estimates based on infinite straight strings for a given impact parameter. A number of new features are identified in the computed microlensing solutions. Our results suggest that optical microlensing can offer a new and potentially powerful methodology for searches for superstring loop relics of the inflationary era.

astro-ph.CO↗

arXiv2013

Modelling non-linear evolution using Lagrangian Perturbation Theory (LPT) re-expansions

We present a new method to calculate formation of cosmological structure in the Newtonian limit. The method is based on Lagrangian perturbation theory plus two key theoretical extensions. One advance involves identifying and fixing a previously ignored gauge-like degree of freedom relating quantities calculated in LPT to those measured by a preferred Friedmann-Robertson-Walker (FRW) observer. Handling this connection between calculational and observer frames is physically essential and ensures a momentum conserving description. The second extension is to systematically re-expand the equations of motion to increase LPT's radius of convergence to the maximum future time prior to orbit crossing. The paper implements a complete algorithm and performs extensive "proof of principle" tests of the new method, including direct comparison to known solutions, evaluation of conserved quantities and formal convergence studies. All are satisfactory. We show convergence is exponential in grid size and Lagrangian order and polynomial in step size. There are three {\it powerful advantages} afforded by the new technique: (1) it employs a smooth representation of all fields and the results are not limited by particle induced shot-noise errors, (2) it permits the numerical error to be controlled by changing Lagrangian order and/or number of steps allowing, in principle, arbitrarily small errors to be achieved prior to orbit crossing and (3) it handles generic cold initial data (any periodic density and velocity fields, including those with initial rotational components). Together, these properties make the new technique well-suited to handle quasi-linear scales where analytic methods and/or numerical simulations fail to provide suitably accurate answers.

astro-ph.CO↗

arXiv2012

Black Hole-Neutron Star Mergers in Globular Clusters

We model the formation of black hole-neutron star (BH-NS) binaries via dynamical interactions in globular clusters. We find that in dense, massive clusters, 16-61% of the BH-NS binaries formed by interactions with existing BH binaries will undergo mergers driven by the emission of gravitational radiation. If the BHs are retained by the cluster after merging with a NS, the BHs acquire subsequent NS companions and undergo several mergers. Thus, the merger rate depends critically upon whether or not the BH is retained by the cluster after the merger. Results from numerical relativity suggest that kick imparted to a ~7 M_sun BH after it merges with a NS will greatly exceed the cluster's escape velocity. In this case, the models suggest that the majority of BH-NS mergers in globular clusters occur within 4 Gyrs of the cluster's formation and would be unobservable by Advanced LIGO. For more massive BHs, on the other hand, the post merger kick is suppressed and the BH is retained. Models with 35 M_sun BHs predict Advanced LIGO detection rates in the range 0.04 - 0.7 per year. On the pessimistic end of this range, BH-NS mergers resulting from binary-single star interactions in globular clusters could account for an interesting fraction of all BH-NS mergers. On the optimistic end, this channel may dominate the rate of detectable BH-NS mergers.

astro-ph.HE↗

arXiv2011

Pseudospectral Calculation of Helium Wave Functions, Expectation Values, and Oscillator Strength

The pseudospectral method is a powerful tool for finding highly precise solutions of Schrödinger's equation for few-electron problems. We extend the method's scope to wave functions with non-zero angular momentum and test it on several challenging problems. One group of tests involves the determination of the nonrelativistic electric dipole oscillator strength for the helium $1^1$S $\to 2^1$P transition. The result achieved, $0.27616499(27)$, is comparable to the best in the literature. Another group of test applications is comprised of well-studied leading order finite nuclear mass and relativistic corrections for the helium ground state. A straightforward computation reaches near state-of-the-art accuracy without requiring the implementation of any special-purpose numerics. All the relevant quantities tested in this paper -- energy eigenvalues, S-state expectation values and bound-bound dipole transitions for S and P states -- converge exponentially with increasing resolution and do so at roughly the same rate. Each individual calculation samples and weights the configuration space wave function uniquely but all behave in a qualitatively similar manner. Quantum mechanical matrix elements are directly and reliably calculable with pseudospectral methods. The technical discussion includes a prescription for choosing coordinates and subdomains to achieve exponential convergence when two-particle Coulomb singularities are present. The prescription does not account for the wave function's non-analytic behavior near the three-particle coalescence which should eventually hinder the rate of the convergence. Nonetheless the effect is small in the sense that ignoring the higher-order coalescence does not appear to affect adversely the accuracy of any of the quantities reported nor the rate at which errors diminish.

physics.atom-ph↗

arXiv2010

Extending the domain of validity of the Lagrangian approximation

We investigate convergence of Lagrangian Perturbation Theory (LPT) by analyzing the model problem of a spherical homogeneous top-hat in an Einstein-deSitter background cosmology. We derive the formal structure of the LPT series expansion, working to arbitrary order in the initial perturbation amplitude. The factors that regulate LPT convergence are identified by studying the exact, analytic solution expanded according to this formal structure. The key methodology is to complexify the exact solution, demonstrate that it is analytic and apply well-known convergence criteria for power series expansions of analytic functions.This analysis fully explains the previously reported observation that LPT fails to predict the evolution of an underdense, open region beyond a certain time. It also implies the existence of other examples, including overdense, closed regions, for which LPT predictions should also fail. We show that this is indeed the case by numerically computing the LPT expansion in these problematic cases. The formal limitations to the validity of LPT expansion are considerably more complicated than simply the first occurrence of orbit crossings as is often assumed. Evolution to a future time generically requires re-expanding the solution in overlapping domains that ultimately link the initial and final times, each domain subject to its own convergence criterion. We demonstrate that it is possible to handle all the problematic cases by taking multiple steps (LPT re-expansion). We characterize how the leading order numerical error for a solution generated by LPT re- expansion varies with the choice of Lagrangian order and of time step size. Convergence occurs when the Lagrangian order increases and/or the time step size decreases in a simple, well-defined manner. We develop a recipe for time step control for LPT re-expansion based on these results.

astro-ph.CO↗

arXiv2010

Pseudospectral Calculation of the Wavefunction of Helium and the Negative Hydrogen Ion

We study the numerical solution of the non-relativistic Schrödinger equation for two-electron atoms in ground and excited S-states using pseudospectral (PS) methods of calculation. The calculation achieves convergence rates for the energy, Cauchy error in the wavefunction, and variance in local energy that are exponentially fast for all practical purposes. The method requires three separate subdomains to handle the wavefunction's cusp-like behavior near the two-particle coalescences. The use of three subdomains is essential to maintaining exponential convergence. A comparison of several different treatments of the cusps and the semi-infinite domain suggest that the simplest prescription is sufficient. For many purposes it proves unnecessary to handle the logarithmic behavior near the three-particle coalescence in a special way. The PS method has many virtues: no explicit assumptions need be made about the asymptotic behavior of the wavefunction near cusps or at large distances, the local energy is exactly equal to the calculated global energy at all collocation points, local errors go down everywhere with increasing resolution, the effective basis using Chebyshev polynomials is complete and simple, and the method is easily extensible to other bound states. This study serves as a proof-of-principle of the method for more general two- and possibly three-electron applications.

physics.comp-ph↗

arXiv2009

Clustering of Superstring Loops

The fragmentation of horizon crossing superstrings creates loops that accrete and bind to collapsing matter perturbations if the string tension is less than a critical value and if the loops are large-scale. For typical model parameters (velocity dispersion of newly formed loops, loop length distribution, etc.) the galactic loop density is greatly enhanced as compared to the universe's mean loop density. The limiting enhancement of loop (energy) density is 0.25-0.4 times the enhancement of cold dark matter (ratio of galaxy to universe's dark matter densities) and is fully achieved for dimensionless string tensions less than 10^-13 at galactic scales less than 100 kpc. The enhancement is substantial for any tension less than the critical value which is of order 10^-9. The fact that the string loop enhancement roughly tracks that of cold dark matter is a robust result for small tension and large-scale fragmentation. Experiments sensitive to the local Galactic population of loops, especially microlensing, should enjoy characteristic detection rates greatly boosted over homogeneous estimates.

astro-ph.CO↗

arXiv2007

Cosmic String Detection via Microlensing of Stars

Cosmic superstrings are produced towards the end of the brane inflation. If the string tension is low enough, loops tend to be relatively long-lived. The resultant string network is expected to contain many loops which are smaller than typical Galactic scales. Cosmic expansion damps the center of mass motion of the loops which then cluster like cold dark matter. Loops will lens stars within the galaxy and local group. We explore microlensing of stars as a tool to detect and to characterize some of the fundamental string and string network properties, including the dimensionless string tension $G μ/c^2$ and the density of string loops within the Galaxy. As $G μ\to 0$ the intrinsic microlensing rate diverges as $1/\sqrt{G μ}$ but experimental detection will be limited by shortness of the lensing timescale and/or smallness of the bending angle which each vary $\propto G μ$. We find that detection is feasible for a range of tensions. As an illustration, the planned optical astrometric survey mission, Gaia, should be able to detect numerous microlensing events for string networks with tensions $10^{-10} \simless G μ\simless 10^{-6}$. A null result for optical microlensing implies $G μ\simless 10^{-10}$. If lensing of a given source is observed it will repeat because the internal motions of the loop are relativistic but the center of mass motion may be much smaller, of order the halo velocity. This distinctive hallmark $\sim 1000$ repetitions, suggests a useful method for confirmation of a potential lensing detection.

astro-ph↗